Stieltjes-Integral Characterizations of Sheffer-Dunkl Polynomial Sequences
This work characterizes Sheffer-Dunkl polynomial sequences (the Dunkl-operator analogue of classical Sheffer sequences) through two Stieltjes moment integrals against functions of bounded variation, extending the classical Thorne and Sheffer integral characterizations to the Dunkl setting. Students learn how a polynomial sequence defined by a differential-difference (Dunkl) operator and Dunkl-kernel generating function can be equivalently described as an integral of associated polynomials against a measure, and how the defining power series is recovered as the moment transform of that measure, linking Sheffer-Dunkl sequences to moment problems.
Two characterizations of Sheffer-Dunkl sequences Alejandro Gil Asensi 1 and Judit M´ınguez Ceniceros
This classical-analysis paper studies Sheffer-Dunkl polynomial sequences, the extension of classical Sheffer polynomial sequences to the Dunkl setting in which the ordinary derivative is replaced by …